In 1959, he was made deputy defense minister.[4] He was appointed defense minister under President Ludvik Svoboda in April 1968, replacing Bohumír Lomský in the post.[2][5][6] Four months after Dzúr's appointment the Soviet Union invaded Czechoslovakia in August 1968.[7]

In the immediate aftermath of the invasion, Dzúr was arrested in his office by two Soviet military officers.[8]Ivan Yershov, Soviet chief of staff during the invasion, stated in 1989 that Dzúr initially refused to take orders from the Soviets, arguing that only Alexander Dubcek, leader of the Czechoslovak communist party, could give orders to him.[7] However, Andrei Grechko, the former commander of the Warsaw Pact, told Dzúr on telephone that "if a single Czechoslovak soldier fired so much as one shot, he would personally hang Dzur from the first tree."[7] Dzúr was allowed only to call Dubcek to inform the invasion.[8] On 28 September 1968 Dzúr increased the number of Czech military areas accessible to Soviet troops.[9]

Dzúr was elected to the communist party's central committee in 1971.[3] His term as defense minister ended on 11 January 1985 when he retired from office due to ill health.[10]Milán Václavík replaced him in the post.[3]